{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:QBYXFLVWA62H4IYS4FPNCXDUBK","short_pith_number":"pith:QBYXFLVW","schema_version":"1.0","canonical_sha256":"807172aeb607b47e2312e15ed15c740a82bcc102ed935c7f2f8bd68151e08241","source":{"kind":"arxiv","id":"1309.0468","version":2},"attestation_state":"computed","paper":{"title":"The induced PBW filtration, Frobenius splitting of double flag varieties, and Wahl's conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"Chuck Hague","submitted_at":"2013-09-02T17:20:24Z","abstract_excerpt":"Let G be a semisimple algebraic group over an algebraically closed field of positive characteristic p. Generalizing the construction of the PBW filtration on Weyl modules for G we construct a G-stable filtration on tensor products of Weyl modules which we call the induced PBW filtration. We use this filtration to give some purely representation-theoretic conditions which are equivalent to the existence of a Frobenius splitting of the double flag variety $G/B \\times G/B$ that maximally compatibly splits the diagonal. In particular, this gives a sufficient condition for Wahl's conjecture to hold"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1309.0468","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-09-02T17:20:24Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"df003e0e12d336e858c4d61381d58a0f8e2e82ae4f76ed71e61bfdc00adc141b","abstract_canon_sha256":"2ad68e9b18bfb0cff921e6af1252dc0d85ab970acb2e355a88feb09b52d38a6e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:32.314244Z","signature_b64":"Yvz5NbJ+FbIIuO7xfI5Srx7SUVhEJtllsbu/NWa0hueKog1UbyaQq1A65lPAutq49fGZX820yJi944M4XlstBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"807172aeb607b47e2312e15ed15c740a82bcc102ed935c7f2f8bd68151e08241","last_reissued_at":"2026-05-18T03:12:32.313536Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:32.313536Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The induced PBW filtration, Frobenius splitting of double flag varieties, and Wahl's conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"Chuck Hague","submitted_at":"2013-09-02T17:20:24Z","abstract_excerpt":"Let G be a semisimple algebraic group over an algebraically closed field of positive characteristic p. Generalizing the construction of the PBW filtration on Weyl modules for G we construct a G-stable filtration on tensor products of Weyl modules which we call the induced PBW filtration. We use this filtration to give some purely representation-theoretic conditions which are equivalent to the existence of a Frobenius splitting of the double flag variety $G/B \\times G/B$ that maximally compatibly splits the diagonal. In particular, this gives a sufficient condition for Wahl's conjecture to hold"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0468","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1309.0468","created_at":"2026-05-18T03:12:32.313640+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.0468v2","created_at":"2026-05-18T03:12:32.313640+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.0468","created_at":"2026-05-18T03:12:32.313640+00:00"},{"alias_kind":"pith_short_12","alias_value":"QBYXFLVWA62H","created_at":"2026-05-18T12:27:57.521954+00:00"},{"alias_kind":"pith_short_16","alias_value":"QBYXFLVWA62H4IYS","created_at":"2026-05-18T12:27:57.521954+00:00"},{"alias_kind":"pith_short_8","alias_value":"QBYXFLVW","created_at":"2026-05-18T12:27:57.521954+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QBYXFLVWA62H4IYS4FPNCXDUBK","json":"https://pith.science/pith/QBYXFLVWA62H4IYS4FPNCXDUBK.json","graph_json":"https://pith.science/api/pith-number/QBYXFLVWA62H4IYS4FPNCXDUBK/graph.json","events_json":"https://pith.science/api/pith-number/QBYXFLVWA62H4IYS4FPNCXDUBK/events.json","paper":"https://pith.science/paper/QBYXFLVW"},"agent_actions":{"view_html":"https://pith.science/pith/QBYXFLVWA62H4IYS4FPNCXDUBK","download_json":"https://pith.science/pith/QBYXFLVWA62H4IYS4FPNCXDUBK.json","view_paper":"https://pith.science/paper/QBYXFLVW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.0468&json=true","fetch_graph":"https://pith.science/api/pith-number/QBYXFLVWA62H4IYS4FPNCXDUBK/graph.json","fetch_events":"https://pith.science/api/pith-number/QBYXFLVWA62H4IYS4FPNCXDUBK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QBYXFLVWA62H4IYS4FPNCXDUBK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QBYXFLVWA62H4IYS4FPNCXDUBK/action/storage_attestation","attest_author":"https://pith.science/pith/QBYXFLVWA62H4IYS4FPNCXDUBK/action/author_attestation","sign_citation":"https://pith.science/pith/QBYXFLVWA62H4IYS4FPNCXDUBK/action/citation_signature","submit_replication":"https://pith.science/pith/QBYXFLVWA62H4IYS4FPNCXDUBK/action/replication_record"}},"created_at":"2026-05-18T03:12:32.313640+00:00","updated_at":"2026-05-18T03:12:32.313640+00:00"}